The classical formulation of libertarianism seems to be incompatible with the requirements of political legitimacy. Some libertarians have endorsed this result, denying that the state is legitimate. This paper argues, however, that the particular nature of that incompatibility represents a problem for the classical formulation of libertarianism. It is argued that acknowledging the existence of a particular minimal form of positive rights might overcome the problem in question. It is further argued that acknowledgment of such positive rights would seem to provide a more adequate normative ground for making sense of some central libertarian insights and concerns.